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Slide Rules

Index by Purpose

While many slide rules were made as general calculating instruments, for multiplying numbers and solving equations with squares, cubes, trigonometric functions, and logarithms, many others were made to ease the calculations associated with a specific task. Click on items in the list below to see rules in the collection with an identifiable specialized purpose. For comparison, a few illustrative examples of all-purpose slide rules are shown under the link to General Calculation.

This paper, brass, and wood cylindrical slide rule has 20 sets of A, B, and C scales, with each set 47 cm in length. The scales are printed on paper that is glued around a sliding brass drum (with wooden handles) and on brass slats that are attached to a round brass frame on either end. The frame is screwed to a wooden base. A sheet of instructions for THACHER'S CALCULATING INSTRUMENT is glued along the top front of the base.

The right side of the paper on the drum is marked in italics: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Divided by W. F. Stanley, London, 1882. Made by Keuffel & Esser Co. N.Y. A small silver metal tag affixed to the front right of the base is engraved: KEUFFEL & ESSER CO. (/) NEW-YORK (/) 663. Wayne Feely has suggested that K&E began manufacturing (as opposed to simply distributing) Thacher cylindrical slide rules in 1887, indicating 1887 is the earliest date for this example of the instrument. The latest date for the instrument is 1900, because K&E changed the design of the brass frame at that time.

The object is contained in a wooden case that bears no identifying marks. According to the accession file, the rule was found in a Smithsonian collections storage locker in the Arts & Industries Building about 1964.

This rule has a cylindrical hollow brass drum, which is covered with paper printed with 40 A scales. The first A scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The paper is also printed in italics on the right side: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Divided by W. F. Stanley, London, 1882. A wooden handle is attached to each end of the drum, and the drum slides in both directions.

The drum fits inside an open rotating frame to which 20 brass slats are fastened. The slats are lined with cloth and covered with paper. The paper on each slat is printed with two B and two C scales. The first B scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The first C scale runs from 100 to 334; the fortieth runs from 308 to 325. The frame is attached to a mahogany base, and the object is housed in a mahogany case. A paper label appears to have been removed from the top of the case.

A paper of directions and rules for operating THACHER'S CALCULATING INSTRUMENT is glued to the top front of the base. A metal tag attached to the top back of the base is engraved: Keuffel & Esser (/) New York. The front right corner of the frame is stamped with numbers: 57 and 35. Presumably one of these is the serial number, but which one is not clear. In either case, the low number and the shape of the frame suggest that this example is the earliest Thacher cylindrical slide rule in the collections. Model 1740 sold for $30.00 in 1887.

Robert B. Steffes of the U.S. Bureau of Labor Statistics donated this instrument to the Smithsonian in 1970.

See also MA*312866 and 1987.0107.08.

References: Wayne E. Feely, "Thacher Cylindrical Slide Rules," The Chronicle of the Early American Industries Association 50 (1997): 125–127; Catalogue of Keuffel & Esser (New York, 1887), 128. This was the first K&E catalog to list the model 1740.

This circular slide rule consists of a silver-colored metal dial, 8-1/2" wide, mounted on a silver-colored metal disc. Three oblong holes on the base disc permit the reading of trigonometric scales on a white celluloid and cardboard disc that is between the metal discs. The celluloid disc is marked: COPYRIGHTED (/) L. ROSS, SAN FRANCISCO (/) PATENTS PENDING.

On the front of the instrument, the top dial is divided along the outer edge into 400 equal parts. In each quadrant of the dial, the scale is marked from 100 to 1,000, with every tenth division marked. Inside of this scale, there is a spiral scale with 25 coils divided logarithmically from 0 to 1,000, making the rule equivalent to a linear slide rule about 50 feet long. These scales are marked in purple and are worn away in several places, including around much of the edge and underneath where the indicators rest.

Affixed to the center of the disc is a brown metal linear rule, 1-1/8" wide, marked with N, M (Sum), D (Difference), and Root scales. This rule is made of three pieces, but the center no longer slides. Also affixed to the center is a yellow celluloid hairline indicator, 3/4" wide, and a second yellow celluloid indicator, 1-1/2" wide. This indicator is marked on the left side by fours from 0 to 100, labeled Quadrants, and on the right side at varying intervals from 100 to 1,000, labeled Nos. It is attached to a metal handle lined with yellow-white celluloid. The handle is also attached to a pivot at the center back of the instrument. The handle is marked: THE ROSS (/) PRECISION COMPUTER (/) Computer Mfg. Co. (/) San Francisco. The handle has reminders for setting the device for multiplication, division, and proportion, and there is a thumbscrew for making adjustments.

The instrument also came with a loose, wedge-shaped piece of yellow celluloid with a hole at one end for attaching to the center of the computer. It is marked with the names of various trigonometric functions and various angles. The round part of the instrument fits into a black leather case with two snaps, stamped both inside and outside: x THE ROSS ÷ (/) PRECISION COMPUTER (/) COMPUTER MFG. CO. (/) SAN FRANCISCO U.S.A. (/) PAT. PEND. COPYRIGHTED. An instruction manual (1996.3077.02) and a letter and advertising literature (1966.3077.03) sent to the purchaser, Roy Kegerreis of New York, were received with this instrument. The letter is dated July 31, 1918, and the manual was copyrighted in 1919.

Louis Ross of San Francisco designed three circular slide rules in the 1910s: the Precision Computer, the Meridi-o-graph, and the Rapid Computer. Advertisements and reports of surviving instruments indicate that the Precision Computer varied in appearance and size.

The Computer Manufacturing Company sold the Precision Computer for $20.00. A clamp for mounting the rule above a desk sold separately for $2.50. The company claimed its customers included the Panama Canal Commission, DuPont Powder Works, and General Electric. The company's offices were originally located on 25 California Street in San Francisco; in 1921, the factory moved from 268 Market to 340 Sansome. The Sansome address is handwritten inside the instruction manual, suggesting Kegerreis learned about the computer in 1918 but did not purchase one until 1921.

Dr. Roy Kegerreis (1886–1968) obtained his BS in Electrical Engineering from The Ohio State University in 1907, his MS in Mathematics from Harvard, and his PhD in Physics from the University of Michigan in 1917. At the time he purchased this slide rule, he apparently was living in New York City. Kegerreis went on to get an MD in 1934, and he worked for many years as a radiologist. This slide rule was given to the Smithsonian by his daughter, in his memory.

This desktop slide rule has a cylindrical brass drum covered with paper printed with 40 A scales. A wooden knob is fastened to each end of the drum. The drum fits in an open rotating brass frame; 20 brass slats span the frame. The right side of the paper on the drum is printed in italics: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Made by Keuffel & Esser Co. N.Y.

The slats are lined with cloth and covered with paper. Each slat is printed with two B and two C scales. The first A scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The first B scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The first C scale runs from 100 to 334; the fortieth runs from 308 to 305.

The front of the frame is spanned by a brass pyramidal bar. A brass and metal mount with three thumbscrews is attached to the bar. The mount may be adjusted by height, and it slides along the bar. A magnifying glass was to be positioned on the mount, but it is missing in this example.

The frame is screwed to a mahogany base. A paper with instructions is glued to the top front of the base. The top back of the base is engraved: KEUFFEL & ESSER Co (encircling N.Y.); 4013 (/) 3518; TRADE MARK (below the K&E lion logo). A sticker on the back of the base is marked: DEPARTMENT OF AGRICULTURE (/) 6076 – AMS. This rule was found in the Smithsonian collections, but it was presumably associated with the Agricultural Marketing Service, an agency established within the U.S. Department of Agriculture in 1939. The rule may have been purchased earlier but not inventoried, since AMS was preceded by several government bureaus, including the Office of Markets, which was founded in 1913.

Keuffel & Esser Company of New York sold versions of the Thacher cylindrical slide rule from about 1883 until about 1950. There were two models, one with a magnifying glass (K&E model 1741 before 1900, K&E model 4013 after) and one without (K&E model 1740 before 1900, K&E model 4012 after). This is a model 4013; the serial number suggests it was manufactured around 1915 and after MA*321789. The marking on the core also no longer references W. F. Stanley, the English firm that originally manufactured the instrument for sale by K&E. Stanley continued to provide the engine-divided scales after K&E began making the rest of the instrument in 1887. K&E took over printing the scales in the 1910s. Model 4013 sold for $45.00 in 1913.

In 1881, Edwin Thacher, a "computing engineer" for the Keystone Bridge Company in Pittsburgh, Pennsylvania, received a patent for an improvement in slide rules. Thacher was a graduate of Rennselaer Polytechnic Institute who spent much of his career designing railway bridges. To assist in his calculations, he designed a cylindrical slide rule. Thacher's rule, though it fit on a desk, was equivalent to a conventional slide rule over 59 feet long. It had scales for multiplication and division and another scale, with divisions twice as large, for use in finding squares and square roots. But it had no trigonometric scales.

To produce his "calculating instrument," Thacher turned to the London firm of W. F. Stanley. The company even designed a special dividing engine for preparing the scales for the instrument. These were printed on paper sheets, which were pasted to the drum and the slats. In this example, the paper is also printed in italics on the right side: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Divided by W. F. Stanley, London, 1882.

The drum is rotated with wooden handles. The cylinder of slats is held in place with a brass frame, which is affixed to a wooden base. A paper of DIRECTIONS AND RULES FOR OPERATING is lacquered to the front of the base. The rear of the base bears a small silver metal label engraved: Keuffel & Esser (/) New York. F. F. NICKEL is painted underneath the base.

Keuffel & Esser Company of New York sold versions of the Thacher cylindrical slide rule from at least 1883 until about 1950. There were two models, one with a magnifying glass (K&E model 1741, later K&E model 4013), and one without (K&E model 1740, later K&E 4012). This is a model 1740. The front right corner of the instrument's metal frame is engraved with the number 107. A paper K&E label on the inside lid of the instrument's mahogany case is marked in ink: 1740/661 (/) Thachers (/) Calculating (/)Instr. The top front of the bottom of the case is also carved with 661. In 1887, the model 1740 sold for $30.00.

Frank Ferdinand Nickel purchased this example around 1883 and donated it to the Smithsonian in 1945, through his son, Henry W. Nickel. The elder Nickel was born in Hanau, Germany, in 1857. He came to the United States around 1883 and worked as a mechanical engineer in New York, Ohio, Pennsylvania, and New Jersey. He also taught at Columbia University in the 1910s. He wrote Direct-Acting Steam Pumps (New York: McGraw-Hill, 1915).

In 1881, Edwin Thacher, a "computing engineer" for the Keystone Bridge Company in Pittsburgh, Pennsylvania, received a patent for an improvement in slide rules. Thacher, a graduate of Rennselaer Polytechnic Institute, spent much of his career designing railway bridges. To assist in his calculations, he designed a cylindrical slide rule. Thacher's rule, though it fit on a desk, was equivalent to a conventional slide rule over 59 feet long. The rule had scales for multiplication and division and another scale, with divisions twice as large, for use in finding squares and square roots. There were no trigonometric scales.

To produce his "calculating instrument," Thacher turned to the London firm of W. F. Stanley. The company even designed a special dividing engine for preparing the scales for the instrument. These were printed on paper sheets, which were pasted to the drum and the slats. In this example, the paper is also printed in italics on the right side: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Divided by W. F. Stanley, London, 1882. Made by Keuffel & Esser Co. N.Y. Wayne Feely has suggested that K&E began manufacturing (as opposed to simply distributing) Thacher cylindrical slide rules in 1887, indicating 1887 is the earliest date for this example of the instrument.

The drum is rotated with wooden handles. The cylinder of slats is held in place with a brass frame, which is affixed to a wooden base. A paper of DIRECTIONS AND RULES FOR OPERATING is glued to the front of the base. A small silver metal tag affixed to the front right of the base is engraved: KEUFFEL & ESSER CO. (/) NEW-YORK (/) 589. A metal extension on the front, screwed to both sides of the frame, bears a fixed holder and thumbscrew that once held a magnifying glass.

A paper K&E label on the inside lid of the instrument's mahogany case is marked in ink: 1741/589 (/) Thacher's (/) Calculating (/) Instr. The inside of the lid and the bottom of the base are both painted: M59. The back of the base is missing a chip 5 cm in length. The left and right sides of the case both bear labels marked in ink: INSTRUMENT (/) CALCULATING (/) THATCHER. A diagonal line is drawn through the second T in "Thatcher" on the right side.

Keuffel & Esser Company of New York sold versions of the Thacher cylindrical slide rule from at least 1883 until about 1950. There were two models, one with a magnifying glass (K&E model 1741, K&E model 4013 after 1900), and one without (K&E model 1740, later K&E 4012). This is a model 1741. In 1892, the model 1741 sold for $40.00. The Physics Department of the United States Military Academy transferred this example to the Smithsonian in 1958.

This desktop slide rule is in a mahogany case. It has a cylindrical brass drum covered with paper printed with forty A scales. A wooden handle is fastened to each end of the drum. The drum fits in an open rotating brass frame; twenty brass slats span the frame. The right side of the paper on the drum is printed in italics: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Made by Keuffel & Esser Co. N.Y.

The slats are lined with cloth and covered with paper. Each slat is printed with two B and two C scales. The first A scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The first B scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The first C scale runs from 100 to 334; the fortieth runs from 308 to 305.

The front of the frame is spanned by a brass pyramidal bar. A brass and metal mount with three thumbscrews is attached to the bar. The mount may be adjusted by height, and it slides along the bar. A magnifying glass was supposed to be positioned on the mount. A brass handle is in the case, but the round glass part is missing.

The frame is screwed to a mahogany base. A paper with instructions is glued to the top front of the base. The top back of the base is engraved: KEUFFEL & ESSER Co (encircling N.Y.); 4013 (/) 3419; TRADE MARK (below the K&E lion logo). A square off-white label inside the lid is printed: KEUFFEL & ESSER CO. (/) NEW YORK HOBOKEN, N.J. (/) CHICAGO ST. LOUIS SAN FRANCISCO MONTREAL (/) DRAWING MATERIALS, SURVEYING INSTRUMENTS (/) MEASURING TAPES (/) No. 4013 (/) SERIAL 3419. Writing on masking tape attached to the top and the front of the case has been covered with black marker. This writing may read in part 6825 and represent the inventory number at the Interstate Commerce Commission, which transferred the object to the Smithsonian in 1962. The Smithsonian catalog number is written on the top of the case in black marker: 321-789.

Keuffel & Esser Company of New York sold versions of the Thacher cylindrical slide rule from about 1883 until about 1950. There were two models, one with a magnifying glass (K&E model 1741 before 1900, K&E model 4013 after) and one without (K&E model 1740 before 1900, K&E model 4012 after). This is a model 4013; the serial number suggests it was manufactured around 1915. The marking on the core also no longer references W. F. Stanley, the English firm that originally manufactured the instrument for sale by K&E. Stanley continued to provide the engine-divided scales after K&E began making the rest of the instrument in 1887. K&E took over printing the scales in the 1910s. Model 4013 sold for $45.00 in 1913.

Compare markings on the core to MA*315663. See also MA*327886 and 1996.3079.01.

This desktop slide rule is in a wooden case that is significantly deteriorated on its inside. The rule has a cylindrical brass drum covered with paper printed with forty A scales. A wooden handle is fastened to each end of the drum. The drum fits in an open rotating brass frame; twenty brass slats span the frame. The right side of the paper on the drum is printed in italics: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Divided by W. F. Stanley, London, 1882. Made by Keuffel & Esser Co. N.Y.

The slats are lined with cloth and covered with paper. Each slat is printed with two B and two C scales. The first A scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The first B scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The first C scale runs from 100 to 334; the fortieth runs from 308 to 305.

The frame is screwed to a mahogany base. A paper with instructions is glued to the top front of the base. An ivory label for Keuffel & Esser Co. is screwed to the front right corner. The top back of the base is engraved: KEUFFEL & ESSER Co (encircling N.Y.); 4012 (/) 1689; TRADE MARK (below the K&E lion logo). Another ivory K&E label is fastened inside the lid of the case. A paper K&E label pasted inside the lid is stamped in faded purple ink: No. 4013 (/) Serial 1689. Written in pencil is: Mar 22/07.

The Thacher cylindrical slide rule was sized for a desk, but its scales were equivalent to those on a conventional slide rule over 59 feet long. It had scales for multiplication, division, and squares and square roots. There were no trigonometric scales.

Keuffel & Esser sold model 4012 from 1900 to about 1950. The markings and serial number indicate this example dates to 1907. Model 4012 cost $35.00 in 1909. The U.S. Department of Agriculture transferred this example to the Smithsonian in 1964.

The brass core of this cylindrical slide rule is covered by paper marked with forty A scales. The core fits in an open rotating frame that holds twenty metal slats; each slat is lined with cloth, covered with paper, and marked with two B and two C scales. Wooden knobs on each end of the core rotate the instrument. The frame is attached to a mahogany base.

The first A scale runs from 100 to 112 and the fortieth runs from 946 to 100 to 105. The first B scale runs from 100 to 112, the last from 946 to 100 to 105. The first C scale runs from 100 to 334, the last from 308 to 305. The paper covering the core is also printed in italics on the right side: Made by Keuffel & Esser Co., New York; Patented by Edwin Thatcher [sic], C.E. Nov. 1st., 1881.

The paper of instructions and rules for operating THACHER'S CALCULATING INSTRUMENT, normally glued to the top front of the base, is coming loose and is torn on this example. A large chip is also missing from the left handle. The top back of the base is stamped: KEUFFEL & ESSER CO. (encircling N.Y.); 4012 (/) 4218; TRADEMARK (below the K&E logo of a lion).

Keuffel & Esser sold versions of the Thacher cylindrical slide rule from about 1883 until about 1950. There were two models, one with a magnifying glass (K&E model 1741 before 1900, K&E model 4013 after) and one without (K&E model 1740 before 1900, K&E model 4012 after). This is a model 4012; the serial number suggests it was manufactured around 1915. The marking on the core also no longer references W. F. Stanley, the English firm that originally manufactured the instrument for sale by K&E. Stanley continued to provide the engine-divided scales after K&E began making the rest of the instrument in 1887. K&E took over printing the scales in the 1910s. Model 4012 sold for $35.00 in 1916, $60.00 in 1922, and $70.00 in 1927.

Compare markings on the core to MA*322730. See also MA*312866 and MA*326628.

The brass core of this cylindrical slide rule is covered with paper marked with forty A scales. The core fits in an open rotating frame that holds twenty metal slats; each slat is lined with cloth, covered with paper, and marked with two B and two C scales. Wooden knobs on each end of the core rotate the instrument. The frame is attached to a mahogany base.

The first A scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The first B scale runs from 100 to 112, the last from 946 to 100 to 105. The first C scale runs from 100 to 334, the last from 308 to 305. The paper covering the core is also printed in italics on the right side: Made by Keuffel & Esser Co., New York; Patented by Edwin Thatcher [sic], C.E. Nov. 1st., 1881.

A paper of instructions and rules for operating THACHER'S CALCULATING INSTRUMENT is glued to the top front of the base. The top back of the base is stamped: KEUFFEL & ESSER CO. (encircling N.Y.); 4012 (/) 4917; TRADEMARK (below the K&E logo of a lion).

Keuffel & Esser sold versions of the Thacher cylindrical slide rule from about 1883 until about 1950. There were two models, one with a magnifying glass (K&E model 1741 before 1900, K&E model 4013 after) and one without (K&E model 1740 before 1900, K&E model 4012 after). This is a model 4012; the serial number suggests it was manufactured around 1920. Model 4012 sold for $35.00 in 1916, $60.00 in 1922, and $70.00 in 1927.

The National Bureau of Standards (now the National Institute of Standards and Technology) declared this object excess property and transferred it to the Smithsonian in 1965. In 1968, the Department of Commerce borrowed the slide rule to exhibit in the U.S. Pavilion at HemisFair, an international exposition held in San Antonio, Tex. According to the accession file, a staffer replaced four missing screws on the base before returning the rule.